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From the lesson

Random Access in Wifi Networks

In this lesson, we will investigate WiFi, another type of wireless network. Rather than having stringent power control algorithms as we saw for cellular, WiFi relies on "random access" methods to manage interference among users in the same location.

Taught By

Christopher Brinton

Lecturer

Mung Chiang

Professor

Transcript

So now, let's look at the throughput. And we just came up with expressions for the probability that a station's going to transmit and the probability that all the other stations aren't going to transmit. So first, let's look at the per-station throughput. So now, again, we said that when we have to have things happen at the same time, we multiply them. So, B is transmitting and A is not transmitting and D is not transmitting and C is not transmitting and E is not transmitting. So it's multiplication. So we basically take probability of transmission, which is probability that A transmits And we multiply that by the probability that none of the other stations are transmitting, and we just saw that before. That was 1 minus PropTrans and then we repeated that multiplication four times, and here we can just raise that to the fourth power. So, now we know in that in general, then if we had, suppose we had ten stations, well then we'd have one transmitting and nine not transmitting, so this would be raised to the ninth power, and if we had one transmitting but, and we had 20 stations it would be one and then 19, so in general let's say that we have, we cal the number of stations in this numstat. And that's we'll send that's the number of stations. So this would be that probtrans times one minus probtrans. [NOISE] And do that multiplication a bunch of times. Times one minus Probtrans and this multiplication happens Numstat minus one because one of those stations is this initial trans station over here. So, that happens numstat minus 1 times, or you can raise it to the numstat minus 1 power. Now, this is the per station throughput. So now, what is the total throughput? So, this is for instance if we looked at B or A or C, D or E independently. But now if we want to look at the total throughput we have to say that we have to add the throughputs of each of the individual stations. So, we just simply add the throughput of B plus throughput of A plus throughput of D plus throughput of C and so on. So we get through of A plus the through-put of B and we keep adding up. And since it's the same equation for each station, we then just get that the total through-put is equal to the number of stations we have times the per-station through-put, very simple. [SOUND] So, if we go back to our example again. Suppose the probability of transmission, [SOUND] was 0.8. So we have Was 20%. So then we convert that into a decimal, we get 0.2. And then the per-station throughput would be equal to the probability of transmission, which is 0.2. Times 1 minus the probability of transmission. And here we have five stations, we'll just assume that [INAUDIBLE] five stations. So we, then we'd have 1 minus 0.2. And we have that four times 1 minus 0.2, times 1 minus 0.2, times 1 minus 0.2. And if you do that out, we get 0.2 times 0.8 times 0.8 times 0.8 times 0.8 again, [INAUDIBLE] broken record here and then that is equal to 0.08192, which is 8.192%, so what that means is that every station is going to get 8% through. Then the total throughput, we would get by multiplying the per-station throughput. By the total number of stations. So the total then, figure this out, would be equal to the per-station times the total number of stations, which is 0.4096 or 40.96%. Lets also point out as well that here we are dealing with throughput in percentages right so we are dealing with them as percent's and in reality we said before that throughput is measured in bytes per second, right so typically we'll see like mega bytes per second and the reason that we are doing in a percent's here it's just comparatively the same. To understand this you have to recall how we get this percentage in the first place. So we're basing this relative to the idea that the maximum throughput we could have is one frame in one time slot. So in each time slot that we have, we could just have one frame. Now, each frame is going to have a certain amount of bits in it and each time slot is going to have a certain amount of seconds. Or it's going to. Actually be fractions of a second. So this is a time slot and this is a frame up here rather than it being a bit and a second that we're talking about. But it's just a multiplicative factor for us to get there. We'll just have to multiply by the number of frames that we have. Per bit, or the other way around. And then we have to multiply by the number of time slots that we have per second in order to get bits per second. And so, in this percentage rate here, when we say 40.96%, we mean that 40.9% of the time slots we are going to have a successful message delivery. And in the other 60%, approximately 60%, we're not going to have a successful message delivery. And in this case right here, we're saying that we have, this is, again, remember this is per station through put. So we're saying Relative to the maximum that this station could get if it was the only station in the network, which is not the case we are getting 8% of what we could in maximum get if we were transmitting successful in each time slot, so usually these percentages are relative to the maximum, or the percentages of the maximum, which would be 100% through-put or meaning that we get one frame in each time slot.

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